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Moderate structural realism about spacetime
 Synthese
, 2008
"... This paper sets out a moderate version of metaphysical structural realism that stands in contrast to both the epistemic structural realism of Worrall and the – radical – ontic structural realism of French and Ladyman. According to moderate structural realism, objects and relations (structure) are on ..."
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Cited by 42 (16 self)
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This paper sets out a moderate version of metaphysical structural realism that stands in contrast to both the epistemic structural realism of Worrall and the – radical – ontic structural realism of French and Ladyman. According to moderate structural realism, objects and relations (structure) are on the same ontological footing, with the objects being characterized only by the relations in which they stand. We show how this position fares well as regards philosophical arguments, avoiding the objections against the other two versions of structural realism. In particular, we set out how this position can be applied to spacetime, providing for a convincing understanding of spacetime points in the standard tensor formulation of general relativity as well as in the fibre bundle formulation. 1. Moderate in contrast to radical structural realism Structural realism is a position in the philosophy of science that has been much debated recently. It is the view that only structure in the sense of the relations that are instantiated in the world is real or at least is all that we can know. The latter position is known as epistemic structural realism, the former one as ontic structural realism (this distinction goes back to
On the Classification of Asymptotic Quasinormal Frequencies for d–Dimensional Black Holes and Quantum Gravity
, 2004
"... We provide a complete classification of asymptotic quasinormal frequencies for static, spherically symmetric black hole spacetimes in d dimensions. This includes all possible types of gravitational perturbations (tensor, vector and scalar type) as described by the Ishibashi–Kodama master equations ..."
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Cited by 38 (2 self)
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We provide a complete classification of asymptotic quasinormal frequencies for static, spherically symmetric black hole spacetimes in d dimensions. This includes all possible types of gravitational perturbations (tensor, vector and scalar type) as described by the Ishibashi–Kodama master equations. The frequencies for Schwarzschild are dimension independent, while for Reissner–Nordström are dimension dependent (the extremal Reissner–Nordström case must be considered separately from the non–extremal case). For Schwarzschild de Sitter, there is a dimension independent formula for the frequencies, except in dimension d = 5 where the formula is different. For Reissner–Nordström de Sitter there is a dimension dependent formula for the frequencies, except in dimension d = 5 where the formula is different. Schwarzschild and Reissner–Nordström Anti–de Sitter black hole spacetimes are simpler: the formulae for the frequencies will depend upon a parameter related to the tortoise coordinate at spatial infinity. We also address non–black hole spacetimes, such as pure de Sitter spacetime—where there are quasinormal modes only in odd dimensions—and pure Anti–de Sitter spacetime—where scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the normal frequencies. Our results match previous numerical calculations with great accuracy. Asymptotic quasinormal frequencies have also been applied in the framework of quantum gravity for black holes. Our results show that it is only in the simple Schwarzschild case
Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories
"... Recently the Master Constraint Programme for Loop Quantum Gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Wheeler – DeWitt constraint equations in terms of a single Master Equation. While the proposal has some promising abstract features, it was until now ..."
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Cited by 37 (16 self)
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Recently the Master Constraint Programme for Loop Quantum Gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Wheeler – DeWitt constraint equations in terms of a single Master Equation. While the proposal has some promising abstract features, it was until now barely tested in known models. In this series of five papers we fill this gap, thereby adding confidence to the proposal. We consider a wide range of models with increasingly more complicated constraint algebras, beginning with a finite dimensional, Abelean algebra of constraint operators which are linear in the momenta and ending with an infinite dimensional, nonAbelean algebra of constraint operators which closes with structure functions only and which are not even polynomial in the momenta. In all these models we apply the Master Constraint Programme successfully, however, the full flexibility of the method must be exploited in order to complete our task. This shows that the Master Constraint Programme has a wide range of applicability but that there are many, physically interesting subtleties that must be taken care of in doing so. In particular,
The case for background independence
, 2005
"... The aim of this paper is to explain carefully the arguments behind the assertion that the correct quantum theory of gravity must be background independent. We begin by recounting how the debate over whether quantum gravity must be background independent is a continuation of a longstanding argument ..."
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Cited by 37 (1 self)
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The aim of this paper is to explain carefully the arguments behind the assertion that the correct quantum theory of gravity must be background independent. We begin by recounting how the debate over whether quantum gravity must be background independent is a continuation of a longstanding argument in the history of physics and philosophy over whether space and time are relational or absolute. This leads to a careful statement of what physicists mean when we speak of background independence. Given this we can characterize the precise sense in which general relativity is a background independent theory. The leading background independent approaches to quantum gravity are then discussed, including causal set models, loop quantum gravity and dynamical triangulations and their main achievements are summarized along with the problems that remain open. Some first attempts to cast string/M theory into a background independent formulation are also mentioned. The relational/absolute debate has implications also for other issues such as unification and how the parameters of the standard models of physics and cosmology are to be explained. The recent issues concerning the string theory landscape are reviewed and it is argued that they can only be resolved within the context of a background independent formulation. Finally, we review some recent proposals to make quantum theory more relational. This is partly based on the text of a talk given to a meeting of the British Association for the Philosophy of Science, in July 2004, under the title ”The relational idea in physics and cosmology.”
Causal evolution of spin networks
 Nucl. Phys
, 1997
"... A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum stat ..."
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Cited by 34 (6 self)
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A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum states of the gravitational field joined together by labeled null edges. The theory exists in 3+1, 2+1 and 1+1 dimensional versions, and may also be interepreted as a theory of labeled timelike surfaces. The dynamics is specified by a choice of functions of the labelings of d+1 dimensional simplices,which represent elementary future light cones of events in these discrete spacetimes. The quantum dynamics thus respects the discrete causal structure of the causal sets. In the 1 + 1 dimensional case the theory is closely related to directed percolation models. In this case, at least, the theory may have critical behavior associated with percolation, leading to the existence of a classical limit.
When do measures on the space of connections support the triad operators of loop quantum gravity
, 2002
"... In this work we investigate the question, under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain nonAbelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its inves ..."
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Cited by 33 (9 self)
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In this work we investigate the question, under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain nonAbelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of “nogo theorems ” asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces. The fluxobservables we consider play an important role in loop quantum gravity since they can be defined without recurse to a background geometry, and they might also be of interest in the general context of quantization of nonAbelian gauge theories. 1
Toward an understanding of flow in video games
 Computers in Entertainment
, 2008
"... In the domain of computer games, research into the interaction between player and game has centred on ‘enjoyment’, often drawing in particular on optimal experience research and Csikszentmihalyi’s ‘Flow theory’. Flow is a wellestablished construct for examining experience in any setting and its app ..."
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Cited by 32 (0 self)
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In the domain of computer games, research into the interaction between player and game has centred on ‘enjoyment’, often drawing in particular on optimal experience research and Csikszentmihalyi’s ‘Flow theory’. Flow is a wellestablished construct for examining experience in any setting and its application to gameplay is intuitive. Nevertheless, it's not immediately obvious how to translate between the flow construct and an operative description of gameplay. Previous research has attempted this translation through analogy. In this article we propose a practical, integrated approach for analysis of the mechanics and aesthetics of gameplay, which helps develop deeper insights into the capacity for flow within games. The relationship between player and game, characterized by learning and enjoyment, is central to our analysis. We begin by framing that relationship within Cowley’s usersystemexperience (USE) model, and expand this into an information systems framework, which enables a practical mapping of flow onto gameplay. We believe this approach enhances our understanding of a player's interaction with a game and provides useful insights for games ’ researchers seeking to devise mechanisms to adapt gameplay to individual players.
Recent developments in nonperturbative quantum gravity, in Quantum Gravity and Cosmology
 Proceedings of the XXIIth GIFT International Seminar on Theoretical Physics
, 1991
"... New results from the new variables/loop representation program of nonperturbative quantum gravity are presented, with a focus on results of Ashtekar, Rovelli and the author which greatly clarify the physical interpretation of the quantum states in the loop representation. These include: 1) The const ..."
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Cited by 31 (7 self)
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New results from the new variables/loop representation program of nonperturbative quantum gravity are presented, with a focus on results of Ashtekar, Rovelli and the author which greatly clarify the physical interpretation of the quantum states in the loop representation. These include: 1) The construction of a class of states which approximate smooth metrics for length measurements on scales, L, to order lPlanck/L. 2) The discovery that any such state must have discrete structure at the Planck length. 3) The construction of operators for the area of arbitrary surfaces and volumes of arbitrary regions and the discovery that these operators are finite. 4) The diagonalization of these operators and the demonstration that the spectra are discrete, so that in quantum gravity areas and volumes are quantized in Planck units. 5) The construction of finite diffeomorphism invariant operators that measure geometrical quantities such as the volume of the universe and the areas of minimal surfaces. These results are made possible by the use of new techniques for the regularization of operator products that respect diffeomorphism invariance. Several new results in the classical theory are also reviewed including the solution of the hamiltonian and diffeomorphism constraints in closed form of Capovilla, Dell and Jacobson and a new form of the action that induces ChernSimon theory on the boundaries of spacetime. A new classical discretization of the Einstein equations is also presented. 1 bitnet address: